The grades on a physics midterm at Springer are normally distributed with $\mu = 73$ and $\sigma = 3.5$. Ben earned a n $81$ on the exam. Find the z-score for Ben's exam grade. Round to two decimal places.
Answer: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Ben's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{81 - {73}}{{3.5}}} $ ${ z \approx 2.29}$ The z-score is $2.29$. In other words, Ben's score was $2.29$ standard deviations above the mean.